My headcanon is that the predator species is mostly peaceful and civilized, and the ones in the movies and comic books are to their advanced galactic civilization what bow hunters are to ours. They have the kind of technology that they could wipe out the Xenomorphs in a heartbeat but the trophy hunters have some sort of lobby that is holding things up. Or maybe they have a lot of environmentalists types and they protect Xenomorphs with the same sort of fervor ours save the whales.

One can safely say that Predators aren't stupid. Knowing this and combining it with what you've said, I feel like the Predators could extinct xenomorphs if they wanted to.
Bears are generally more dangerous than people. People train bears in the circus. The reason they feel this is safe is because humans are ultimately in control. If the human race ever felt threatened by bears we could take them all out. But we don't do this because its a waste of time and resources and the bear problem isn't a problem.
Predators, as a species, aren't threatened by xenomorphs at all. They probably could extinct them if they really wanted to, but it'd be as ultimately pointless as humans extincting bears. And some of the predators are really into killing xenomorphs because there's nothing they've discovered in the universe that's as menacing. So this really cements the idea that predators are at the top of the food chain and are just dicking around with humans and xenomorphs because they've run out of threatening enemies.